Extrude multiple Shapes along the same Curve
As far as I know this is currently unsupported, since curve geometry itself and Bevel Object are both part of Object Data.
Maybe this will eventually be supported when Library Overrides project is merged, until then here are two workarounds.
Workaround 1 - Curve deform modifier
Use bevel objects on independent &quot;dummy curves&quot; with a simple straight geometry, but set handles to Free or Automatic so there are enough geometry subdivisions.
Now to each of these dummy curves add a Curve Modifier and set it to an independent instance of the same &quot;deforming curve&quot; sharing object data. There must be one instance of &quot;deforming curve&quot; for each &quot;dummy&quot;, both at the same world space coordinates, so deformations are undistorted.
Easiest way to set this up is probably to complete a single &quot;curve bundle&quot; and then clone both around and just change the bevel object.

Cons: The dummy curves wont keep up with severe length changes from the deformations, only shape changes.
Workaround 2 - Array + Curve deform modifier
Slightly extrude your &quot;section defining curves&quot; so they have a small but non zero height, then add an Array Modifier set to Fit Curve on Z axis.
Pick a &quot;path defining curve&quot; as curve to fit. Now add a Curve Modifier set to the same curve object on Z axis.
Clone this modifier setup around to different &quot;section curves&quot;, but always set the &quot;path defining curve&quot; to an instance of the original one so they always copy the same path shape. Once again make sure objects using Curve Modifiers are always coincident with their deforming curves.
Cons: Since this relies on an Array Modifier there will always be a slight  difference (as little as the extruded height of the section) in length between deforming curve and the actual profile. Decreasing height will improve precision at the expense of performance.